Optimal-arrangement-based four-scanning-heads error separation technique for self-calibration of angle encoders

Conventional methods for the calibration of angle encoders typically only consider the graduation error of the encoder's circular scale. However, the radial motion of the circular scale during its rotation, due to its eccentricity and the axis of rotation radial error motion, can also introduce noticeable errors to the angle measurement in most practical applications. Based on the analysis of the influence of radial motion, an optimal-arrangement-based four-scanning-heads error separation technique for in situ self-calibration of angle encoders is presented. This Fourier-based technique uses the basic self-calibration model to measure the first-order Fourier component of the encoder error which includes the contribution of eccentricity. Meanwhile, the separation technique is utilized to separate the residual Fourier components of the graduation error from the measurement deviation due to radial error motion. The effect of the scanning heads' angular position errors on the calibration results is discussed. Optimal arrangements of the four heads are achieved to avoid the suppression of the Fourier components, and reduce the propagation of errors. Numerical results and experimental comparisons demonstrate the effectiveness of the proposed method. Moreover, this technique can also be used for measuring the spindle radial error motion for some users.